Why is the simulated climatology of tropical cyclones so sensitive to the choice of cumulus parameterization scheme in the WRF model?

Abstract

The sensitivity of simulated tropical cyclones (TCs) to the choice of cumulus parameterization (CP) scheme in the advanced Weather Research and Forecasting Model (WRF-ARW) version 3.5 is analyzed based on ten seasonal simulations with 20-km horizontal grid spacing over the western North Pacific. Results show that the simulated frequency and intensity of TCs are very sensitive to the choice of the CP scheme. The sensitivity can be explained well by the difference in the low-level circulation in a height and sorted moisture space. By transporting moist static energy from dry to moist region, the low-level circulation is important to convective self-aggregation which is believed to be related to genesis of TC-like vortices (TCLVs) and TCs in idealized settings. The radiative and evaporative cooling associated with low-level clouds and shallow convection in dry regions is found to play a crucial role in driving the moisture-sorted low-level circulation. With shallow convection turned off in a CP scheme, relatively strong precipitation occurs frequently in dry regions. In this case, the diabatic cooling can still drive the low-level circulation but its strength is reduced and thus TCLV/TC genesis is suppressed. The inclusion of the cumulus momentum transport (CMT) in a CP scheme can considerably suppress genesis of TCLVs/TCs, while changes in the moisture-sorted low-level circulation and horizontal distribution of precipitation are trivial, indicating that the CMT modulates the TCLVs/TCs activities in the model by mechanisms other than the horizontal transport of moist static energy.

1 Introduction

State-of-the-art numerical models with cumulus parameterization (CP) schemes are widely used to simulate tropical cyclone (TC) climatology and future projections (Knutson et al. 2013; Wu et al. 2014; Manganello et al. 2014; and many others). Sensitivity of the simulated TC activities to CP schemes is frequently reported in the literature (Slingo et al. 1994; Zhang and McFarlane 1995; Smith 2000; Vitart et al. 2001; Lin et al. 2008; Oouchi et al. 2006; Murakami et al. 2012; Zhao et al. 2012; Lim et al. 2015). Several previous studies attempted to suppress the parameterized deep convection to increase TC numbers by increasing the threshold of minimum entrainment rate in their simulations (e.g., Kim et al. 2012; Zhao et al. 2012; Lim et al. 2015). Suppressing the parameterized deep convection by entraining more dry air into the mass-flux plume leads to cooling and drying in the mid-upper troposphere, along with enhanced surface latent heat flux and moistening in the lower troposphere. The resulting increase in conditional instability provides an environment more favorable for TC-like vortices (TCLV) to develop (Lim et al. 2015). However, the further increase of the entrainment rate is prohibitive to TC genesis (Zhao et al. 2012), indicating the complexity of TC genesis with regard to CP scheme in numerical model simulations.

In addition to these thermodynamic factors in a CP scheme, some dynamical factors could also influence TC genesis in weather and climate models. The inclusion of the cumulus momentum transport (CMT, defined as cumulus friction) was reported to improve the TC track forecasts in the Navy Operational Global Atmospheric Prediction System (NOGAPS) (Hogan and Pauley 2007) and the TC intensity forecasts in the Global Forecast System (GFS) (Han and Pan 2006). Han and Pan (2006) also noticed a reduction of spurious storm genesis in their 132-h forecast when the CMT in their CP scheme was turned on. Oouchi et al. (2006) showed significant influence of the strength of CMT on the simulated TC numbers in their 20-km-mesh global atmospheric model. In addition, the divergence damping term artificially added to the momentum equations is another factor that could significantly influence TC genesis (Zhao et al. 2012). A more recent study by Reed et al. (2015a) showed that the dynamical core has a remarkable impact on storm intensity and genesis frequency as well.

TC genesis is largely controlled by convective organization both in nature and in atmospheric models. Convective self-aggregation plays an important role in multiscale moist convective organization and thus is thought to play a role in TC genesis (Bretherton et al. 2005; Muller and Held 2012; Wing and Emanuel 2014; Muller and Bony 2015; Wing et al. 2017). The self-aggregated moist patches can spontaneously organize and develop into TCs in the presence of ambient rotation (Nolan et al. 2007; Khairoutdinov and Emanuel 2013; Davis 2015; Wing et al. 2016). Although convective self-aggregation is evident in radiative-convective equilibrium (RCE) simulations using non-rotating cloud-resolving models (CRMs) with typical 2–3 km horizontal resolution (Bretherton et al. 2005; Muller and Held 2012; Muller and Bony 2015; Wing and Cronin 2015), it is still meaningful to link convective self-aggregation to TC activities when a CP scheme is applied in a regional climate model. This is because convective self-aggregation has also been found in RCE simulations using regional or global models with parameterized convections (e.g., Held et al. 2007; Popke et al. 2013; Becker and Stevens 2014; Reed et al. 2015b).

A few physical processes have been identified as contributors to convective aggregation in CRMs. It has been suggested that diabatic feedback is necessary and the cloud–longwave radiation feedback is essential for convective self-aggregation to occur (Bretherton et al. 2005; Muller and Held 2012), although the relative importance of high versus low clouds is disputed (Bretherton et al. 2005; Muller and Held 2012; Arnold and Randall 2015; Muller and Bony 2015). The vertical structures of clouds and humidity in drier and moister regions can affect the radiative heating profile and thus convective self-aggregation (Muller and Held 2012; Wing and Emanuel 2014; Emanuel et al. 2014; Muller and Bony 2015; Bretherton and Khairoutdinov 2015). Muller and Bony (2015) noted that low clouds in dry regions help support strong low-level radiative cooling and subsidence into the boundary layer in dry regions, while middle and high clouds in regions with deep moist convection induce anomalous mid-tropospheric radiative heating that reinforces rising motion in convective regions. Therefore, the induced circulation between dry and moist regions depends on the vertical structure of radiative cooling/heating in these regions. The vertical structure of this circulation in turn affects the dynamically driven tendency of column moist static energy (MSE) variance and the transport of moist static energy from dry to moist regions, and thus the strength of convective self-aggregation. A useful method to visualize convective self-aggregation is to bin subregions of humidity from dry to wet, then plot bin-means of vertical mass flux versus humidity bin and height (Bretherton et al. 2005; Muller and Held 2012; Wing and Emanuel 2014; Bretherton and Khairoutdinov 2015; Muller and Bony 2015). The circulation, especially the low-level circulation shown as the streamfunction in a height and sorted moisture space and its associated MSE transport, is believed to be important to convective self-aggregation. The low-level circulation is a feature of self-aggregation, and its advection of MSE upgradient is one of the processes that controls self-aggregation.

In this study, the sensitivity of the simulated climatology of TCs to the choice of CP schemes in the advanced Weather Research and forecasting (WRF-ARW) model will be interpreted using concepts originally devised in idealized studies of convective self-aggregation. We will show how the strength of the moisture-sorted low-level circulation differs in the simulations with different CP schemes examined and how it is related to genesis of TC-like vortices (TCLVs) and thus TCs in various simulations. In addition, the effects of CMT and shallow convection in CP schemes on convective self-aggregation and thus the simulated TCLV/TC activities will also be evaluated. The remainder of the paper is organized as follows. Section 2 describes the methodology and data employed in this study, including a summary of numerical experiments conducted for the western North Pacific (WNP) with different CP schemes using the WRF-ARW model. In Sects. 3 and 4, results from the four standard CP schemes and those from five sensitivity experiments are discussed in detail, respectively. Finally, Sect. 5 provides a summary of our main findings.

2 Methodology and data

2.1 Model description

The WRF-ARW version 3.5 (Skamarock et al. 2008) is used in this study. The model atmosphere is discretized with 35 full terrain-following σ levels in the vertical with the model top at 20 hPa. The model domain mainly covers the WNP region with a horizontal resolution of 20 km (see Fig. S1). The WRF Single-Moment 6-Class (WSM6) microphysics scheme (MP) with six prognostic cloud variables is used for grid-scale cloud microphysics processes (Hong and Lim 2006). The shortwave and longwave radiation fluxes are calculated using the RRTMG radiation scheme (Iacono et al. 2008). The Yonsei University (YSU) planetary boundary layer (PBL) scheme (Hong et al. 2006) is used for subgrid-scale vertical mixing. The Noah land surface model (LSM) is used for land surface processes (Chen and Dudhia 2001). Four CP schemes in the WRF-ARW model are selected for the sensitivity experiments in this study (Table 1), including the original modified Tiedtke scheme (TDK1), the latest new modified Tiedtke scheme which is identical to the version released in WRF3.8.1 (TDK2), the Kain–Fritsch scheme (KF), and the Betts–Miller–Janjic scheme (BMJ). Note that all CP schemes have both deep and shallow convection components but only the two Tiedtke schemes include the cumulus momentum transport (CMT).

Table 1 The CP schemes used in the standard experiments

The model initial and lateral boundary conditions for the model atmosphere were obtained from the Modern-Era Retrospective Analysis for Research and Applications (MERRA) reanalysis data from the National Aeronautics and Space Administration (NASA), which covers the satellite era from 1979 to the present and has achieved significant improvements in precipitation and water vapor climatology (Rienecker et al. 2011). The MERRA data have a horizontal resolution of 0.5° latitude by 0.67° longitude and are available at 31 pressure levels from 1000 to 10 hPa at 6-h intervals. The European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis Interim data provided the initial conditions for soil temperature and moisture (Dee et al. 2011). The sea surface temperature (SST) was updated daily using the 0.25° × 0.25° global analysis provided by National Oceanic and Atmospheric Administration (NOAA; Reynolds et al. 2010). The diurnal SST variation was calculated based on the surface energy budget with the method documented by Zeng and Beljaars (2005).

2.2 Experimental design

The WRF-ARW version 3.5 outlined above was used to conduct ten seasonal simulations (1990–1999; from June 29 to November 01 for each season) over the WNP (Fig. S1). The first 2 days were considered as model spin-up period and will not be included in our analyses hereafter. In a total, nine experiments were performed. In the four standard experiments the default CP schemes listed in Table 1 were used. In addition to the standard experiments, five sensitivity experiments were performed to evaluate the effects of cumulus momentum transport (CMT) and shallow convection in CP schemes on the simulated TC climatology (Table 2). In TDK1_NoCMT and TDK2_NoCMT, the CMT was turned off in TDK1 and TDK2, respectively. In KF_CMT, a CMT parameterization scheme (see “Appendix”) was implemented into the KF scheme. In TDK1_NoCMT_NoSH, both the CMT and shallow convection parameterizations were turned off in the original TDK1 scheme. Finally, in KF_NoSH, the shallow convection parameterization in the standard KF scheme was turned off.

Table 2 List of sensitivity experiments

2.3 Detection algorithm for TCLVs/TCs

TCs and TCLVs were detected in model simulations using the 6-h model outputs. The detection algorithm used the following criteria based on those reported in Nguyen and Walsh (2001) but with some modifications in order to match the 20-km horizontal resolution.

• a. The maximum relative vorticity at 850 hPa exceeds 2.0 × 10⁻⁴ s⁻¹.

• b. There is a minimum sea level pressure (SLP) center with closed isobar within the radius of 300 km of the maximum relative vorticity center at 850 hPa. The radius of the averaged minimum SLP system is at least 100 km. The closed isobar drops at least 1 hPa to the minimum SLP center.

• c. There is a warm core within 300 km of the minimum SLP center and the warm core has the temperature within the 100 km radius at least 0.1 K warmer than the temperature between 100 and 300 km averaged between 700 and 300 hPa.

• d. For the TC detection, two extra criteria were added: (1) the maximum 10-m wind speed in the lifetime is larger than 17 m s⁻¹ and the genesis time is defined as the time when the maximum 10-m wind speed becomes larger than 17 m s⁻¹; (2) the duration of each detected storm must exceed 48 h.

The small modifications of the above criteria may slightly change the detected TCLVs and TCs, but the overall results discussed below are not strongly dependent on those small changes, and hence the conclusions from the following analysis are robust.

2.4 TC best-track data

The best-track data from Joint Typhoon Warning Center (JTWC) were employed in this study. JTWC uses a 1-min averaging period for wind speed in the dataset. The simulated wind speed is basically the mean wind speed in one time step, e.g., 100 s in our simulations. Furthermore, due to the finite-differencing, the model only can resolve time scales larger than two-time steps. This means that the model maximum winds can be considered as a mean in at least 3 min. This needs to be kept in mind when we compare TC intensity in our simulations and that in the best track data.

3 Results for the default CP schemes

3.1 Climatology of the simulated TCLVs/TCs

The simulated ten-season TC tracks and ten-season mean TC numbers by the default CPs are shown in Fig. 1. The simulated seasonal mean TC number by KF is 45.7 (Fig. 1c), which is much more than the observed (19.7 TCs). The simulated seasonal mean TC number by BMJ is 24.2 (Fig. 1b), but the tracks are not as smooth as those simulated by other CPs. The simulated TC numbers by TDK1 (Fig. 1f) and TDK2 (Fig. 1h) are 25.0 and 16.1, respectively, which are about 27% more and 18% less than the observed, respectively.

Fig. 1

The observed (a) and simulated (b–h) TC tracks for ten seasons. The intensity of TCs is represented by Saffir–Simpson scale in colors. The dots are TC genesis locations. The asterisk means the default settings in the official WRF release. ‘A’ donates the mean value of annual TC number averaged in ten seasons and ‘R’ donates the correlation coefficient of TC numbers in the ten seasons between the observation and simulation

Figure 2a shows the interannual variations of the simulated seasonable mean TC numbers over the WNP. KF remarkably over-simulated TC numbers every year. The TC numbers simulated by other three schemes are closer to those observed. In all four schemes, TDK2 has the highest correlation coefficient of 0.74 with observations, while TDK1 only shows a correlation coefficient of 0.05.¹ The other two schemes, namely BMJ and KF, have correlation coefficients of 0.52 and 0.49, respectively. Note that although previous studies showed that the ensemble mean from multiple simulations with different initial conditions could potentially improve the simulated interannual frequencies of TCs (Knutson et al. 2007; Wu et al. 2012), we do not expect the correlation would be dramatically changed among the simulations with the four standard CP schemes.

Fig. 2

The interannual variations of TC numbers from 1990 to 1999 (a) and annual mean TC numbers for each binned lifetime maximum near surface wind speed (b) in simulations with different CP schemes and in observations

Figure 2b shows the seasonal mean TC numbers versus the binned lifetime maximum near surface wind speeds. It is not surprising that the 20 km horizontal resolution with CPs cannot simulate TCs stronger than 70 m s⁻¹. KF shows two peaks: one between 25 and 30 m s⁻¹ and the other between 45 and 50 m s⁻¹. By contrast, BMJ shows only one peak between 20 and 25 m s⁻¹. Both TDK1 and TDK2 have a large peak between 40 and 50 m s⁻¹, and a small peak between 20 and 25 m s⁻¹. KF simulated the largest number of TCs in almost all intensity bins. We noticed that except for TDK2 all schemes simulated more TCs with the intensity between 25 and 55 m s⁻¹ than in observations (BMJ simulated slightly less TCs with the intensity between 45 and 50 m s⁻¹). Since the TC detection algorithm is not particularly sensitive for strong TCs, the result that TDK1, KF and BMJ over-simulated the seasonal TC numbers is robust.

The simulated TCLVs better reflect the general tendency for a particular scheme to develop organized convection because the criteria are less strict than that for TCs. As shown in Fig. 1, most TC genesis are located in the domain of 5°–20°N, 130°–180°N. Hence we only analyzed the characteristics of TCLVs in this area. The seasonal mean number of TCLVs was defined as the number averaged in ten seasons of the accumulated frequency occurrence in 6 h outputs in a simulation. TDK1 simulated the largest number of ten-season mean TCLVs (773), while KF simulated the second largest number of TCLVs (720) and TDK2 simulated the smallest number (201) of TCLVs (Table 3). Both KF and TDK1 consistently simulated more TCLVs than BMJ and TDK2 in all years (Fig. 3a; Table 3).

Table 3 The ten-season mean (standard deviation) values for the numbers of TCLV, the mean size of TCLV, the accumulated TCLV sizes (ATS), and the ratio of TCLVs that belong to TCs

Fig. 3

The interannual variations of the simulated TCLV numbers (a), mean TCLV size (b), mean accumulated TCLV size (c), and the ratio of TCLVs that belong to TCs (d). The TCLV size is defined as the radius of the outermost closed isobar of SLP. The mean accumulated TCLV size is defines as the total TCLV sizes in each season. All TCLVs are counted within the domain (5°N–20°N, 130°E–180°)

To examine the sensitivity of the simulated size of TCLVs/TCs to the choice of a CP scheme used, we also defined the size of a TCLV as the radius of the outermost closed isobar of sea level pressure (SLP). The size of TCLVs/TCs is significantly influenced by the environmental conditions, especially the environmental humidity (Hill and Lackmann 2009). The interannual variations of TC sizes are generally consistent across the CP schemes, such as in the years of 1995, 1997, 1998, and 1999 (Fig. 3b). We further defined the accumulated TCLV sizes (ATS) by adding all TCLVs’ sizes (Fig. 3c). BMJ and TDK2 show very similar interannual variations and seasonal mean values of the ATS. Similar to the number of TCLVs, TDK1 shows the largest ATS and KF has the second largest ATS. The ratio of the TCLVs that belong to TCs is presented in Fig. 3d. The ratio for BMJ is the lowest (36%, Table 3). The ratios for KF, TDK1 and TDK2 are 68, 51 and 60%, respectively, in the ten-season mean (Table 3). TDK1 shows the smallest standard deviations of the ratio as well as the relatively small standard deviations of the TCLV number and size; therefore, we speculate that TDK1 is the least sensitive to the environmental conditions in all four CPs. This explains well why the interannual TC numbers in TDK1 are poorly correlated with observations. In contrast, TDK2 shows the highest correlation coefficient for TC numbers with observations and also high standard deviations of the simulated TCLV numbers, sizes, and the ratio of TCs to TCLVs.

3.2 Characteristics of the moisture-sorted low-level circulation

The simulated TCLVs/TCs likely reflect the general degree of organization of convection. Here we follow the analysis methods documented in Bretherton et al. (2005) and Bretherton and Khairoutdinov (2015) to examine the strengths of the moisture-sorted low-level circulation, which are believed to be important to convective self-aggregation. Bretherton et al. (2005) found that the export of frozen moist static energy (FMSE) out of dry regions during self-aggregation was strong. The latent heat of fusion will not be included in our analysis because we only focus on the low-level circulation in this study. The moist static energy (MSE) is defined as:

$$MSE={C_p}T+gz+{L_v}{q_v},$$

(1)

where C_p is the isobaric specific heat of dry air, T is temperature, g is gravitational acceleration, z is height, L_v is latent heat of vaporization, q_v is water vapor mixing ratio. Following Bretherton et al. (2005), Bretherton and Khairoutdinov (2015), and Muller and Bony (2015), we first sorted the column relative humidity CRH = W/W_sat, where W_sat is the precipitable water assuming saturation of the entire grid column given its temperature profile. We then divided the domain (5°N–20°N, 130°E–180°) into blocks of 160 km by 160 km square area and averaged values in each block. We put all the 6-h instantaneous values in one array, then sort the array from the lowest to the highest values and equally divide the sorted array into 100 bins, and finally average values in each bin.

The streamfunction Ψ introduced by Bretherton et al. (2005) can be used to infer the circulation between the driest and wettest binned CRHs. The 100 CRH bins are sorted from the lowest to highest and given an index from 1 to 100. Starting from Ψ₀(z) = 0, and:

$${{\mathbf{\Psi }}_{\varvec{i}}}\left( {\varvec{z}} \right)={{\mathbf{\Psi }}_{{\varvec{i}} - 1}}\left( {\varvec{z}} \right)+{{\varvec{w}}_{\varvec{i}}}\left( {\varvec{z}} \right)\overline {{{\varvec{\rho}_{\varvec{i}}}\left( {\varvec{z}} \right)}} ,$$

(2)

where w is vertical velocity, z is height, and $\overline {\varvec{\rho}}$ is air density. Ψ_i(z) can be interpreted as the net upward mass-flux at height z accumulated over the ith bin from driest bin. Note that the streamfunction does not represent circulation in physical space but is designed to allow the investigation of the transport between the dry and moist regions, often called the moisture-sorted circulation.

Figure 4 shows the averaged CRH-sorted streamfunction map together with MSE based on all ten-season simulations by the four CP schemes, respectively. The streamfunction map clearly shows two circulations, namely a deep circulation throughout the troposphere and a shallow circulation in the lower troposphere. Both are anticlockwise, suggesting the transport of high MSE from dry regions to wet regions in the lower troposphere, which is favorable for convective self-aggregation. The MSE transport occurs mainly in the boundary layer where MSE is high. Note that the streamfunction, thus the circulation, is not particularly sensitive to any year for a given CP scheme (see Figs. S2–S5, which show the same streamfunction and MSE maps in all individual years for the four CP schemes). The streamfunctions here resemble those found in CRM simulations (e.g., Bretherton et al. 2005; Muller and Bony 2015; Muller and Held 2012).

Fig. 4

The streamfunction (dashed contours for counterclockwise, solid contours for clockwise, every 0.02 kg m⁻² s⁻¹) and MSE (shaded in K) simulated in TDK1 (a), TDK2 (b), KF (c) and BMJ (d). All variables are CRH-sorted (x-axis) by all the 6-h 160 km × 160 km blocks in ten season simulations in the domain (5°–20°N, 130°–180°N) and plotted as a function of height and CRH

TDK1 shows a relatively strong and deep CRH-sorted low-level circulation, which is basically associated with the strong updraft in the wet region and strong downward motion in the dry region (Fig. 4a). The circulation in TDK2 is much weaker than that in TDK1. Nevertheless, the transport of high MSE still occurs below 900 hPa from dry regions to wet regions (Fig. 4b). The overall strength of the CRH-sorted circulation in KF lies in between TDK1 and TDK2 (Fig. 4c). Note that not only does the strength of the low-level circulation matter, but also the height of the circulation is important since the MSE is a strong function of height (Muller and Bony 2015). The low-level circulation in KF is centered at a relatively lower level than that in either TDK1 or TDK2. This suggests that the transport of low-level high MSE from dry regions to wet regions is quite effective in KF since the main transport corridor is located well below 900 hPa where the highest MSE is located (Fig. 4c). BMJ shows a CRH-sorted circulation quite different from that in other schemes (Fig. 4d). First, the deep circulation in BMJ is centered at a considerably lower level than that in any of the other schemes (400 versus 300 hPa) and also located on the drier side than in other schemes. Second, although the low-level circulation in BMJ looks as strong as in TDK1, the lowest part of circulation sits above the high MSE in dry region. This leads to an inefficient transport of low-level high MSE air from dry into wet (often convective) regions (Fig. 4d).

Previous studies have demonstrated that the CRH-sorted low-level circulation is diabatically driven, in particular by both evaporative and radiative cooling associated with low-level clouds in dry regions (e.g., Bretherton et al. 2005; Bretherton and Khairoutdinov 2015; Muller and Bony 2015). To understand the differences in the CRH-sorted low-level circulation among the four CP schemes, we compared distributions of diabatic heating in the CRH-sorted bin and height space from all four experiments (Fig. 5). TDK1 simulated the largest cooling in dry regions with the maximum cooling rate in the subsidence branch of the low-level circulation among all four schemes. TDK2 simulated the weakest cooling with no local enhancement of cooling near the top of the low-level circulation, consistent with the weakest low-level circulation among the four schemes. KF simulated strong cooling as well, similar to TDK2, but with slightly weaker cooling rate near the top of the low-level circulation. In sharp contrast, BMJ simulated strong diabatic cooling in dry regions but largely biased in the mid-lower troposphere although a shallow cooling layer appears in the subsidence branch of the low-level circulation, similar to that in TDK1. The distribution of diabatic cooling explains well the strength of the CRH-sorted low-level circulation.

Fig. 5

The streamfunction (dashed black contours for counterclockwise, solid black contours for clockwise, every 0.02 kg m⁻² s⁻¹) and diabetic heating (shaded in K day⁻¹) simulated in TDK1 (a), TDK2 (b), KF (c) and BMJ (d). All variables are CRH-sorted (x-axis) by all the 6-h 160 km × 160 km blocks in ten season simulations in the domain (5°–20°N, 130°–180°N) and plotted as a function of height and CRH

We further examine contributions of diabatic cooling in dry regions by various physical processes, including radiative heating/cooling, cloud evaporative cooling, and parameterized convection heating/cooling (including both shallow and deep convections). Figure 6 shows the CRH-sorted streamfunction map together with longwave radiative heating/cooling (shading) and cloud condensate (white contour) based on all ten-season simulations by the four CP schemes, respectively. TDK1 has a layer of low-level clouds in dry regions, and this low cloud layer gradually becomes deeper toward the wetter regions (Fig. 6a). The layer of low-level clouds significantly promotes longwave radiative cooling (Fig. 6a). In contrast, there are no distinct layers of low-level clouds in dry regions for TDK2 and KF (Fig. 6b, c). As a result, the clear sky longwave radiative cooling is dominant in the lower troposphere in dry regions for these two CP schemes. BMJ also has a thin layer of low-level clouds in dry regions, but the longwave radiative cooling associated with low-level clouds is weak (Fig. 6d). Overall, TDK2 has the weakest longwave radiative cooling from middle to upper troposphere in dry regions among the four CP schemes.

Fig. 6

Same as Fig. 5 except for the longwave radiative heating rate in color (K day⁻¹). The white contours represent the cloud condensate (staring form 1 mg kg⁻¹ with contour interval of 10 mg kg⁻¹)

Evaporative cooling from cloud microphysics scheme occurs almost everywhere from lower to middle troposphere for all four CP schemes (Fig. 7). Evaporative cooling from cloud liquid is particularly large between 850 and 700 hPa for TDK1 in dry regions (Fig. 7a), which is related to the low-level cloud layer. Evaporative cooling is mild for TDK2 and KF in dry regions (Fig. 7b, c), while very weak evaporative cooling can be found in dry regions for BMJ (Fig. 7d). For CP schemes, the evaporative cooling associated with low-level clouds is parameterized in BMJ (Fig. 8d). Additional evaporative cooling can be found in dry regions for TDK1 (Fig. 8a). The evaporation of the detrained liquid water in the inversion layer with dry environmental condition is explicitly parameterized in TDK1 (Zhang et al. 2011), but not in TDK2 (Zhang and Wang 2017). No explicitly parameterized evaporation of cloud liquid is conducted in KF either. Therefore, there is no evaporative cooling in the troposphere above cloud base for both TDK2 and KF (Fig. 8b, c). The cooling effect associated with low-level clouds thus contributes significantly to the subsidence branch of the CRH-sorted low-level circulation. Note that the warming by BMJ for deep convection shows a jump from large heating rate to near zero at about 500 hPa. Similar results can also be found in Sun et al. (2014). It seems to be a problem of the BMJ scheme implemented in the WRF model, where the cloud top in BMJ is not allowed to the level less than 450 hPa.

Fig. 7

Same as Fig. 5 except for the diabatic heating rate from cloud microphysics scheme in shading

Fig. 8

Same as Fig. 5 except for diabatic heating rate from the cumulus parameterization (CP scheme in shading)

3.3 Characteristics of precipitation versus column RH

The tropical precipitation and column humidity are highly correlated in the near-global cloud-resolving simulations as shown in Bretherton and Khairoutdinov (2015). They found that the perturbations in the FMSE are positively correlated with the perturbations in precipitation in all scales. For example, the precipitating cumulus cloud systems produce radiative heating and surface flux anomalies that have a positive feedback onto the FMSE anomalies and thus precipitation. By using satellite passive microwave measurements, Bretherton et al. (2004) verified that precipitation favors in the moistest regions in the deep tropics.

Based on observational fitting, Bretherton et al. (2004) obtained the following relationship between precipitation and CRH,

$$\frac{{Precipitation}}{{{W_{sat}}}}=b{e^{aCRH}},~~a=15.6,~~b=1.14~ \times {10^{ - 6}}.$$

(3)

Figure 9 shows the scatter plots for precipitation against CRH in all simulations. The blue dots correspond to values in each 160 × 160 km block for daily precipitation normalized by W_sat for ten seasons. The yellow curve is for the CRH bin-average over all blocks for the corresponding simulation. The light blue line is the observational fitting from Eq. (3). The mean precipitation intensity at high CRH columns are close to observations (Fig. 9a–d). KF is the closest to the observations in both dry and wet region. TDK1 shows almost no precipitation when CRH is less than 0.5. It is evident in general that less precipitation in dry regions benefits the organization of convections while relatively large precipitation in dry regions would offset the general downward motion and is unfavorable for low-level clouds and the associated radiative and evaporative cooling, and hence unfavorable for the organization of convections.

Fig. 9

Scatter plot of daily mean CRH versus the scaled precipitation P/W_sat for each CP scheme using spatial 160 km × 160 km block-averages in the domain (5°–20°N, 130°–180°N) in the whole seasonal simulation. The light purple line is for the observational fitting, and the orange curve is for the CRH bin-average in simulations

4 Results from sensitivity experiments

4.1 Climatology of the simulated TCLVs/TCs

The total seasonable mean TC number increased to 49.1 and 22.9 with the CMT turned off in TDK1_NoCMT (Fig. 1e) and in TDK2_NoCMT, respectively (Fig. 1g). With the inclusion of a CMT in KF_CMT, the seasonable mean TC number decreased from 45.7 to 13.0 (Fig. 1d). This demonstrates that the parameterized CMT in a CP scheme can reduce the simulated TC frequency. Note that the CMT parameterizations in KF, TDK1 and TDK2 were implemented differently due to the different formula and entrainment and detrainment rates in each scheme (see “Appendix”) and thus show different degrees in the effect of CMT. The tendencies of zonal (u) and meridional (v) component of wind speed averaged in the domain (5°–20°N, 130°–180°N) and in all ten seasons are shown in Fig. 10. In general, TDK2 has the weakest CMT while TDK1 and KF have larger CMT above cloud base (the sixth model layer and below are typically sub-cloud layers in Fig. 10). Accordingly, the numbers of TCLVs decreased for all three CPs. Interestingly, the size of TCLVs all increased. TDK1 increased 21 km, KF increased 25 km and TDK2 increased 20 km (Table 3). Due to the CMT, the same surface maximum wind speed requires lower sea level pressure (see Fig. S6). The ratios of the TCLVs that belong to TCs all decreased by 16% for both TDK1 and KF, and by 4% for TDK2 (Table 3).

Fig. 10

The tendencies of zonal wind (red curve) and meridional wind (blue curve) averaged in the domain (5°–20°N, 130°–180°N) for ten seasons

Shallow convection is parameterized in all default four CP schemes. We chose TDK1 and KF schemes to test the impact of the parameterized shallow convection on the simulated TCLVs/TCs. The procedure to determine whether there is convection and what kind of convection for each column in the model domain is called “trigger function”. For the first guess, in the TDK1 scheme an undiluted surface air parcel is tested. If the air parcel reaches the lifted condensation level with buoyancy larger than 0.5 K, the grid is considered having active deep or shallow convection. If the convergence of moisture in the boundary layer is larger than the surface evaporation rate, the grid is marked as deep convection, otherwise shallow convection. After the first guess, deep convection and shallow convection are given different entrainment and detrainment rates in quasi-equilibrium cloud updraft. If the cloud depth is thicker than 1.5 km, the grid is finally considered with deep convection, and otherwise with shallow convection. The procedure to find deep and shallow convection in KF scheme is described in Kain (2004). Note that the definition of deep and shallow convections and the boundary between shallow and deep convection are different due to different trigger function deployed in the different CP schemes.

With the parameterized shallow convection turned off in KF_NoSH and TDK1_NoCMT_NoSH, the simulated TC numbers considerably decreased to 30.4 (Fig. 1i) and 34.4 (Fig. 1j), respectively. Accordingly, the number of TCLVs decreased 194 for TDK1_NOSH and 212 for KF_NOSH (Table 3). The size of the TCLVs also decreased 27 km for TDK1_NOSH and 32 km for KF_NOSH. The ratio of the TCLVs that belong to TCs is reduced by 6% for TDK1_NOSH and by 10% for KF_NOSH, respectively (Table 3). This indicates that shallow convection in a CP scheme favors TC genesis in model simulations.

4.2 Characteristics of the moisture-sorted low-level circulation

The inclusion of the CMT in CP schemes generally will not change the CRH-sorted low-level circulation (Fig. 11). The low-level high MSE in dry regions is still exported efficiently to wet regions. Diabatic cooling in dry regions remains almost the same with and without the CMT for all three schemes. The precipitation rate versus CRH (Fig. 12) shows almost no changes with and without the CMT for all three CP schemes either, indicating that the inclusion of a CMT in a CP scheme will not change the thermodynamic related characteristics in the model atmosphere.

Fig. 11

The experiments without (a–d) or with CMT (e, f). The streamfunction (dashed black contours for counterclockwise, solid black contours for clockwise, every 0.02 kg m⁻² s⁻¹) and MSE (shaded in K in a, c, e) and diabatic heating rate (shaded in K day⁻¹ in b, d, f). All variables are CRH-sorted by all the 6-h 160 km × 160 km blocks in ten season simulations in the domain (5°–20°N, 130°–180°N), and plotted as a function of height and CRH

Fig. 12

Daily mean CRH versus the scaled precipitation P/W_sat for each CP scheme using spatial 160 km × 160 km block-averages in the domain (5°–20°N, 130°–180°N) in the whole seasonal simulations. The light purple line is for the observational fitting. The orange (red) curve is for the CRH bin-average without (with) CMT

In sharp contrast to CMT, the CRH-sorted low-level circulation is much weaker without shallow convection in the TDK1_NOSH simulation (Fig. 13a, b). The low-level high MSE in dry regions is located below 900 hPa, indicating that the boundary layer in dry regions is very low with the lack of active shallow convection (Fig. 13a). The shallow, wet boundary layer in dry regions is covered by a thin layer of low-level clouds because the vertical mixing by shallow convection is ignored (see Fig. S7a). Those low level clouds produce the diabatic cooling effects (Fig. 13b), maintaining the CRH-sorted low-level circulation in the TDK1_NOSH experiment. This low-level circulation is still able to flush the low-level high MSE from dry regions to wet regions. Similar pattern is found in the KF_NOSH experiment (Fig. 13c, d, Fig. S7b). Figure 14 shows the precipitation rate versus CRH for TDK1 (TDK1_NOSH) and KF (KF_NOSH). Without parameterized shallow convection, the CRH bin-averaged precipitation rate is much higher in dry regions for both TDK1_NOSH and KF_NOSH. Therefore, without shallow convection, isolated deep convections are likely to occur intermittently in dry regions for a particular CP scheme.

Fig. 13

Same as Fig. 11 but for the CPs (TDK1_NoCMT and KF) without shallow convection (NoSH)

Fig. 14

Same as Fig. 12 except the orange (red) curve is for the CRH bin-average with (without) shallow convection

5 Conclusions

In this study, we compared ten seasonal simulations of TCLVs/TCs over the WNP by four different CP schemes in the WRF-ARW model version 3.5, including the newer Tiedtke scheme (TDK2) publically released since version 3.7. We found that different CP schemes performed very differently in the simulations of TCLVs/TCs. The differences include the number of TCLVs/TCs, the size of TCLVs, the ratio of TCLVs that belong to TCs, and the intensity of the simulated TCs.

The difference in the simulated TCLVs/TCs can be easily understood by the capability of simulating the moisture-sorted low-level circulation that is important to convective self-aggregation (Muller and Bony 2015). Consistent to the simulated TCLVs/TCs activities, the low-level circulation between the dry columns and wet columns shows very different strengths among all four CP schemes examined. TDK1 simulated the strongest low-level circulation and accordingly the largest number of TCLVs, while TDK2 simulated the weakest low-level circulation and thus the least number of TCLVs/TCs. Not only does the strength of the low-level circulation matter, but also its height. This is because the transport of MSE from dry regions to wet regions is largely determined by the height of the low-level circulation. In spite that there is a strong moisture-sorted low-level circulation in the simulations with BMJ, the low-level branch of the circulation is too high and cannot efficiently transport the low-level high MSE from dry columns to wet columns.

The low-level clouds in dry regions play an important role in enhancing the low-level circulation. The low-level clouds provide strong longwave radiative and evaporative cooling effects. The diabatic cooling at the cloud top near and below the inversion layer makes the air mass above to sink, which acts as the driver of the low-level circulation. The most typical scheme having the strongest low-level circulation among all four CP schemes is TDK1. The evaporative cooling significantly contributes to diabatic cooling in dry regions and a strong low-level circulation in BMJ. TDK2 simulates no distinct layer of low-level clouds and consequently it shows the weakest low-level circulation. KF simulates the strength of diabatic cooling in the lower troposphere in dry regions just in between TDK1 and TDK2. Together with the relatively strong diabatic cooling in the mid-upper troposphere in dry regions, the lower part of the low-level circulation in the simulation with KF is well maintained. This circulation below 900 hPa is able to efficiently transport high MSE from dry regions to wet regions.

The horizontal distribution of precipitation is important for self-aggregation in light of the findings by Bretherton and Khairoutdinov (2015). Although all simulations show biases in the overall relationship between precipitation and CRH compared to the observational fitting, they do produce suppressed precipitation in dry regions.

For a particular CP scheme, the low-level circulation is mostly controlled by the treatments of deep and shallow convections. Therefore the low-level circulation is a unique trademark of each CP scheme. The low-level circulation can be weakened by the removal of shallow convection in a CP scheme. Without parameterized shallow convection, considerable precipitation may occasionally occur in dry regions. Relatively large precipitation in dry regions would offset the general downward motion and is unfavorable for the self-aggregation. The reduction of the simulated TCLVs/TCs in a CP scheme by introduction of a parameterized CMT is not accompanied with either the weakening of the low-level circulation or the increase of precipitation in dry regions. This indicates that the CMT modulates the TCLVs/TCs activities in the model by mechanisms other than a low-level circulation that transports MSE.

Results from this study strongly suggest that a CP scheme can be tuned to better simulate the TCLVs/TCs in a climate model. This partially answers the question raised by Tobin et al. (2013) who claimed that most CP schemes do not explicitly include the representation of mesoscale organization. Nevertheless, our results demonstrate that some CP schemes can represent the mesoscale organization quite well in the tropics with 20-km horizontal grid spacing in the WRF-ARW model in terms of the simulated TCLVs/TCs activities. In addition to deep convection, our results also suggest that care needs to be taken for both shallow convection and CMT in a CP scheme in order to realistically simulate the climatology and interannual variability of TCs.

Appendix A

In all experiments with CMT, the CMT is calculated in each grid cell with convection, and the resulting tendency is added to the zonal and meridional momentum equations. The tendency of the CMT can be expressed as (Gregory et al. 1997),

$$\left( {\frac{{\partial U}}{{\partial t}}} \right)_{{cu}} = g\frac{\partial }{{\partial p}}\left[ {M_{u} U_{u} + M_{d} U_{d} - (M_{u} U_{d} )\overline{U} } \right],$$

(4)

where the subscripts u and d depicts updraft and downdraft averaged quantities, respectively. The overbar represents an environmental average. M is the mass flux assuming the updraft and downdraft areas constitute a very small fraction of the grid box. U is the horizontal component of zonal or meridional wind, g is the gravitational acceleration rate, and p is the air pressure.

The CMT parameterizations are different across CP schemes mainly due to the implementation of entrainment and detrainment in the cloud model. The cloud model is described as:

$$- g\frac{{\partial M_{u} U_{u} }}{{\partial p}} = E_{u} \overline{U} - D_{u} \overline{U} + PGF_{u},$$

(5)

$$- g\frac{{\partial M_{d} U_{d} }}{{\partial p}} = E_{d} \overline{U} - D_{d} \overline{U} + PGF_{d} ,$$

(6)

where E is the entrained mass flux and D is the detrained mass flux. PGF is the pressure gradient term. Note that PGF_u and PGF_d are equal to zero in TDK1 but the pressure gradient effects were represented by an enhanced entrainment rate in the updraught equations for E_u and D_u, namely,

$$E_{u} = E_{u} + \lambda D_{u} ,$$

(7)

$$D_{u} = D_{u} + \lambda D_{u} ,$$

(8)

where $\lambda = 2$ for deep and mid-level convection in TDK1.

Gregory et al. (1997) parameterized the PGF based on the following empirical relationships,

$$PGF_{u} = - C_{u} M_{u} \frac{{\partial U}}{{\partial p}},$$

(9)

$$PGF_{d} = - C_{d} M_{d} \frac{{\partial U}}{{\partial p}},$$

(10)

where C_u and C_d are tunable parameters. In TDK2, PGF_u is parameterized as (9) but PGF_d is zero. If we used the enhanced entrainment/detrainment rate to parameterize pressure gradient effects as in TDK1, the domain averaged tendency profile resembles that calculated using formula (9) with C_u = 0.4. We found that C_u = 0.7 or even higher is an optimal value for TDK2.

For the KF scheme, the tendency due to the CMT is simply expressed as:

$$\left( {\frac{{\partial U}}{{\partial t}}} \right)_{{cu}} = g\frac{\partial }{{\partial p}}\left[ {M_{u} U_{u} + M_{d} U_{d} - (M_{u} U_{d} )\overline{U} } \right] - \overline{\omega } \frac{{\partial U}}{{\partial z}},$$

(11)

where, $\overline{\omega }$ is a value related to vertical advection (Kain and Fritsch 1990, 1993).